Conventionally, there is known a system for purifying NOx in an exhaust gas of an internal combustion engine by arranging a SCR (Selective Catalytic Reduction) catalyst in an exhaust pipe of the internal combustion engine and injecting urea as a reducing agent to the SCR catalyst. For this purification system, it has been proposed to estimate the amount of ammonia occluded and stored in the SCR catalyst (hereinafter referred to as “ammonia occlusion amount”) and control the amount of injection of the ammonia based on the estimated ammonia occlusion amount (see, for example, Patent Document 1: Japanese Laid-Open Patent Application Publication No. 2014-111918).